Indeed, @MangshorJhol. DSD is at Junior Conservatoire, as well as one of the most academic schools in the UK, which consistently sends 30 %+ to oxbridge/ ivys. She practises probably 30mins a day max! Lessons (private) once a week, as well as playing opportunities in school and JD. She adores music and the current plan is a career in music.
however, one of her classmates, who actually got into JD before she did, is a different matter. She has been pushed pushed pushed, and is now deeply unhappy and ragingly jealous of those for whom music (and academics) come naturally.
OP, the kind of music setup you want just doesn't exist here, unless you go to a very specialist music school like the Purcell or Menuhin; though I suspect you would disapprove of their Uni outcomes ;-) and even then they wouldn't offer daily lessons.
A prep at the academic level you want may well facilitate a lot of music, but certainly not 1-1 lessons in 2 instruments every day. Even the specialist music schools like the Menuhin don't do that. They suggest one 2 hour lesson on first study a week, sometimes more, alongside class lessons, and one lesson a week on second study, with practice supervision available (the majority of students board).
if you are aiming high academically, there are plenty of academic preps in London that also take music seriously, just not as badly pressured as your OP suggested you want - for good, musically and academically sound reasons.